General actions of hyperstructures and some applications

Chvalina, Jan; Hošková-Mayerová, Šárka; Nezhad, Akbar Dehghan

doi:10.2478/auom-2013-0004

Cited by 22 publications

(23 citation statements)

References 6 publications

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“…Proof. The proof is rather obvious thanks to the straightforward correspondence between relations "≤ M " and "≤ e " suggested by (3) and correspondence between the definition of minimum and maximum of matrices using infima and suprema of their entries. If (S, inf, sup) is distributive, then distributive laws are valid for all a ij , b ij , c ij ∈ S, i.e.…”

Section: And Duallymentioning

confidence: 99%

“…Lemma 2 verifies commutativity, associativity and idempotency. The absorption laws hold thanks to the relationship between ≤ M and ≤ e , expressed by (3), and the fact that (S, inf, sup, ≤ e ) is a lattice. Now that we have established the context of M m,n (S), we define two pairs of dual hyperoperations on M m,n (S) using (3) and (4), or (5), respectively.…”

Section: Min-max Hyperstructures Of Matricesmentioning

confidence: 99%

“…These had been constructed by a number of authors including Borzooei, et al, Chvalina, Davvaz, Dehghan Nezhad, Hošková and others [1,3,9,11] (see also book [8], sections 8.3 and 8.4.) before they were studied from the theoretical point of view [20,21,22].…”

Section: Introductionmentioning

confidence: 99%

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From lattices to Hv-matrices

Křehlík

Novák

2016

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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In this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices. First of all, we define hyperoperations similar to those used when constructing hyperstructures from quasiordered semigroups. This then enables us to show that if entries of matrices are elements of lattices, these considerations provide a natural link between matrices, some basic concepts of the hyperstructure theory including Hv-rings and Hv-matrices and also one recent construction of hyperstructures.

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Section: And Duallymentioning

confidence: 99%

Section: Min-max Hyperstructures Of Matricesmentioning

confidence: 99%

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From lattices to Hv-matrices

Křehlík

Novák

2016

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…A Krasner hyperring is a nonempty set R endowed with a hyperoperation (the addition) and a binary operation (the multiplication) such that (R, +) is a canonical hypergroup, (R, ·) is a semigroup and the multiplication is distributive with respect to the addition. The theory of these hyperrings has been developing since the beginning of seventies, thanks to the contributions of Mittas [14,15], Krasner [10], Stratigopoulos [20], till nowadays [2,3,5,8,13,17].…”

Section: Introductionmentioning

confidence: 99%

Composition hyperrings

Cristea

Jančić-Rašović

2013

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…In this context, we may refer to interesting articles [5] of Cristine Flaut and [6] of Jan Chvalina,Šárka Hošková-Mayerová, and Dehghan Nezhad.…”

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confidence: 99%

Construction of the Smallest Common Coarser of Two and Three Set Partitions

Potůček

2014

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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This paper is inspired by a text of the book [7] ("Úvod do algebry" in Czech, "Introduction to Algebra" in English) of the authors Ladislav Kosmák and Radovan Potůček. They followed the great work of Professor Otakar Borůvka in the field of the partition theory, groupoids and groups and gave them in the context to contemporary modern algebra. Academian Borůvka have deduced and proved many results concerning the partition theory in his publications.His first works [1] and [2] were published during World War II and his monographs [3] and [4] were released in the post-war years.In this paper we deal with a construction of the smallest common coarser of two set partitions associated with equivalence relations, we give a special relation used in the construction and an illustration of blocks of this coarser.Remark 1. Algebra of binary relations was worked up by Jacques Riguet in 1948 (see [8], the translation into Russian has its origin from 1963). Professor Borůvka was rightfully proud himself on his theory of partitions and an appliance of the algebra of relations has never used. From twenty-seven chapters of the book [4] is six devoted to the general theory of partitions and in the chapter 14 and 21 -24 are paragraphs dealing with partitions in the theory of grupoids and groups.

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General actions of hyperstructures and some applications

Cited by 22 publications

References 6 publications

From lattices to Hv-matrices

From lattices to Hv-matrices

Composition hyperrings

Construction of the Smallest Common Coarser of Two and Three Set Partitions

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